There aren't really any suitable nicknames for Chana.
Famous people named Chana:
Actress Chana Eden; poet Chana Bloch; author Sarah Chana Radcliffe; sculptor Chana Orloff.
To pronounce this name accurately, the "Ch" sound should be a guttural sound from the throat. But since that isn't a familiar sound to the English language, Chana is often pronounced SHAY-na.